Zero-order diffractive filters (ZOFs), sometimes dubbed resonant gratings or guided mode resonant filters, are optical filters that are based on the resonant reflection of a leaky waveguide. Illuminated for example with non-polarized, polychromatic light, ZOFs can exhibit characteristic colour effects upon rotation and are therefore clearly identifiable. D. Rosenblatt et al. describe such ZOFs in “Resonant Grating Waveguide Structures”, in IEEE Journal of Quantum Electronics, Vol. 33, No. 11, 1997.
ZOFs employ a layer of a high-index refraction material that has a diffractive microstructure defining at least one of its waveguiding boundaries. The diffractive microstructure features a period Λ and a depth t. The period Λ is in most cases smaller than the wavelength of light for which ZOF is designed.
The resulting waveguiding layer respective of the high-index refraction material has a thickness c and is made of a material having an index of refraction nhigh that is higher than index of refraction (nlow) of the matter surrounding the high-index refraction material. The matter surrounding the high-index refraction material is therefore herein referred low-index refraction matter.
In order to obtain zero-order diffraction colour effects that are recognizable by the human eye, a number of parameters have to be adjusted including grating period Λ, grating depth t, thickness c of the waveguiding layer, fill factor or duty cycle f.f.=p/Λ, grating profile or shape (rectangular, sinusoidal, triangular or more complex) and the indices of refraction of the high-index refraction material nhigh and the low-index refraction matter nlow. More specifically, in order to obtain waveguiding properties typical of ZOFs, the index of refraction of the high-index refraction material nhigh may have to be at least higher by a value of 0.1 compared to the index of refraction of the low-index refraction matter nlow. The high-index refraction matter is thus sometimes dubbed high-index wave guiding layer or simply waveguiding layer.
Depending on the desired properties of the ZOF, the low-index refraction matter has different indices of refraction. For example, a first low-index refraction matter can be made of a solid substrate, whilst a second low-index refraction matter can be ambient air. The second low-index refraction matter may have a different index of refraction than the solid substrate. The diffractive grating can therefore be exposed to ambient air.
For some implementations, ZOFs include a plurality of alternatingly arranged layers of high-index refraction material and low-index refraction matter and/or gradient index of refraction material.
Referring to FIG. 1, a ZOF 100 as known in the art comprises in the x/y-plane a waveguiding layer 120 having lower boundary 122 engaging with a substrate 110. Upper boundary 121 of waveguiding layer 120 is formed as a diffractive grating 125, which includes a plurality of protrusions 127 that are spaced apart from one another, and which is at the interface between waveguiding layer 120 and ambient air 130. The physical properties of diffractive grating 125 are at least defined by its physical dimensions, and more specifically, by its grating period Λ, the width p of protrusions 127 and thickness c of waveguiding layer 120. The fill factor (ff) or duty cycle of diffractive grating 125, can be defined as ff=p/Λ, which may be approximately equal 0.5 or 50%. Waveguiding layer 120 has an index of refraction that is higher than that of air and that of substrate 110. Thusly configured, at least some of polarized or unpolarized polychromatic visible light 150 incident on diffractive grating 125 at an illumination angle Θin is coupled in waveguiding layer 120. Specifically, ZOF 100 may enable the resonant coupling of light of several diffraction orders and thus of several wavelengths into waveguiding layer 120. The diffraction orders and the wavelengths that will be coupled into waveguiding layer 120 depend on at least one parameter of diffractive grating 125, the thickness c of waveguiding layer 120 and differences in the index of refraction between waveguiding layer 120, substrate 110 and ambient air 130″.
The resonant coupling of incident light 150 into waveguiding layer 120 is schematically shown and exemplified as “+1” order light 153 and “−1” order light 154 having orders +1 and −1, respectively. Due to the higher index of refraction of high-index refraction material 120 compared to the one of ambient air 130 and substrate 110, “+1”-order light 153 and “−1”-order light 154 are totally internally reflected from upper boundary 121 and lower boundary 122 of waveguiding layer 120. However, a first portion of the zeroth-order (hereinafter: first zeroth-order light) 151 of incident light 150 is directly transmitted through waveguiding layer 120 and leaves ZOF 100 by propagation through substrate 110. In addition, a second portion of the zeroth-order (hereinafter: second zeroth-order light) 152 of light 150 is diffracted together with “−1” order light 154 into waveguiding layer 120. Both second zeroth-order light 152 and “−1”-order light 154 propagate in waveguiding layer 120 in opposite directions. After propagating over a distance d in waveguiding layer 120, second zeroth-order light 152 is coupled out via diffractive grating 125.
“+1“ order light 153 and “−1” order light 154 may continue propagating in high-index refraction material 120. In contrary to what is true for diffraction orders that are higher than zero, the angle Θout (which is defined with respect to the normal N of waveguiding layer 120) of the outcoupled second zeroth-order light 152 is equal to Θin. This is the reason why the effect is called zero-order diffraction”.
These amendments correct typographical errors which appear in the published application. These amendments do not add new matter to the application.
The resonance condition for the outcoupling of first zeroth-order light 151 and second zeroth-order light 152, can be tailored for a certain wavelength or wavelength spectrum for the outcoupled light. For example, the wavelength(s) of second zeroth-order light 152 outcoupled via diffraction grating 125 depends both on the viewing angle Θout and the rotational orientation φ of diffractive grating 125 with respect to a viewing direction 160. For each pair of angles φ and Θout a particular spectral range or colour is reflected or transmitted.
The spectral characteristics of such ZOFs are therefore tuneable. The reflection spectra Rzero-order or transmission spectra Tzero-order are the most prominent examples of the spectral characteristics of ZOFs. As long as the materials employed in a ZOF possess no substantial absorption, the transmission spectra are the complement of those in reflection.
Additional reference is now made to FIGS. 2 to 7, which schematically show side view illustrations of respective ZOFs as known in the art, the profile of the corresponding index of refraction in Z-direction, and the profile in Z-direction of the corresponding VE multilayer design, assuming homogeneous layers in the X-Y-plane with the respective averaged indices of refraction.
More specifically, FIG. 2 schematically illustrates a side view of a second ZOF 200 which includes high-index refraction material 220 that is disposed between upper and lower low-index refraction matter 210. Second ZOF 200 possesses diffractive rectangular grating lines of depth t on both the upper and lower interfaces of high-index refraction material 220 with low-index refraction matter 210. First the corresponding index of refraction profile 250 shows a step like increase from nair to nmatrix followed by a step like increase to nmat/WG. With respect to an VE first ZOF 201, the index of refraction in the grated area of first ZOF 200 is in first approximation the average of the indices of high-index refraction material 200 and low-index refraction matter 210 weighted by the fill factor ff of rectangular grating profile 225. The configuration of second ZOF 200 results in a VE waveguiding layer 221.
With respect to VE second ZOF 201, the following equation applies:nmat/WG=(1−ff)×nlow+ff×nWG  (1)
The core of VE waveguiding layer 221 has an index of refraction nWG. The symmetric design of second ZOF 200 and the fill factor of 50% results in the same steps in the indices of refraction on the lower side of second ZOF 200. Such a design can be realised e.g. by embossing the grating lines in a substrate followed by a vacuum coating of a high-index refraction material with the mass thickness c. Evaporation of ZnS or sputtering of TiO2 are two examples. Finally a relatively thick top layer with nlow needs to be disposed. In second ZOF 200 the thickness c has to be thicker than the depth t of rectangular grating profile 225.
As is schematically illustrated with respect to VE second ZOF 201, a VE third layer 223 is obtained. Second ZOF 200 includes therefore a VE multilayer design comprising three layers, namely a core layer 223 having an index of refraction of nWG, two adjacent layers both having indices of refraction nmat/WG and the layer of low-index refraction matter 210 having indices of refraction nMatrix. All three layers have indices of refraction which are higher than nair. Thus the thickness deff-WG of effective VE waveguiding layer 221 equals c+t. Typically the distance dair-WG from the air-matrix interface 211 to VE waveguiding layer 221 is much larger than the effective thickness deff-WG of VE waveguiding layer 221.
Making further reference to FIG. 3, a side view of a third ZOF 300 that is free of a holohedral waveguide core is schematically illustrated. In contrast to second ZOF 200, thickness c of high-index refraction material 320 has to be lower compared to the grating depth t. As a result, third ZOF 300 implements a VE multilayer design that includes an upper and a lower VE waveguiding layer 321 separated from one another and each having a thickness c and an index of refraction nmat/WG.
The thickness deff-WG of each VE waveguiding layer 321 is c, and they are separated by an interlayer of 324 having thickness t−c. Typically thicknesses t and c may be of the same order. Light guided in upper VE waveguiding layer 321 interacts with light guided in lower VE waveguiding layer 321.
Additionally referring now to FIG. 4, the design of a fourth ZOF 400 is analogous to the design of third ZOF 300, with the difference that fourth ZOF 400 is free of the top layer of low-index refraction matter 410. Thus, high-index refraction material 420 interfaces with ambient air 430. Index of refraction profile 450 of fourth ZOF 400 schematically illustrates a step like increase from nair to nair/WG followed by a decrease to nair/mat. Other than that, the index of refraction profile 450 is the same as the index of refraction profile 350 schematically illustrated in FIG. 3. Accordingly, VE fourth ZOF 401 is similar to VE third ZOF 301.
Further reference is made to FIG. 5. A fifth ZOF 500 as known in the art comprises a high-index refraction material 520 that is one-sidedly grated with a lower diffraction grating 525, whereas the upper side of high-index refraction material 520 with respect to a viewing direction 160 is flat. This is in distinct contrast to the ZOFs schematically illustrated in the FIGS. 1-4, wherein the high-refraction refraction material is two-sidedly grated.
Fifth ZOF 500 exhibits an asymmetric index of refraction profile. Fifth ZOF 500 can be realised e.g. by embossing, diffraction grating 525 into low-index refraction matter 510 followed by providing high-index refraction material 520 by wet coating. Two examples of such wet coatings are gravure printing of formulations with high-index polymers like Optimate HR751 or with nitrocellulose mixed with TiO2 nano-particles. Finally, a top layer of low-index refraction matter 510 with nlow is provided onto high-index refraction material 520. The design of fifth ZOF 500 results in a VE waveguiding layer 521 having a thickness deff-WG that equals is c+t. The mass thickness c of VE waveguiding layer 521 equals the thickness ch of the holohedral part of high-index refraction material 520 plus grating depth t weighted by the fill factor, as is outlined in the equation below:c=ch+ff×t  (2)
Reference is now made to FIG. 6. A sixth ZOF 600 features a design that is mirrored with respect to fifth ZOF 500. Accordingly, sixth ZOF 600 is free of a lower virtual equivalent (VE) layer having an index of refraction nmat/WG. Sixth ZOF 600 can be realised e.g. first by wet coating a fiat substrate 610 with an embossable high-index refraction material 620, where after coating, the diffraction grating 625 is embossed.
Additional reference is now made to FIG. 7. A seventh ZOF 700 as known in the art employs diffraction gratings 725 having a different cross-sectional grating profile, namely a corrugated profile. Other possible profiles of diffraction gratings 725 include sinusoidal or triangular profiles. In diffraction grating 725: c>t. The index of refraction profile shows gradient variations due to the rounded grating lines of diffraction grating 725. The index of refraction of holohedral core of high-index refraction material 720 is denoted nWG.
Reference is now made to FIGS. 8A, 8B and 8C schematically showing different planar grating profiles. Hitherto, ZOFs that are based on diffraction gratings having linear grating lines (FIG. 8A) with respect to their top view, which shows the x-y plane, have been discussed. Top views of other types of grating structures are schematically illustrated in FIG. 8B and FIG. 8C. More specifically, FIG. 8B schematically illustrates a top view of a crossed grating structure of a chessboard-like type, and FIG. 8C schematically illustrates a top view of a hexagonal dot grating structure. Parameters p, px and py, denote the structure size of high-index refraction material 820. Λ, Λx and Λy are the periods of these microstructures in the x-y-plane.
Patent document EP1560884 teaches a pigment, the smallest size of which corresponds at least to a multiple of the greatest wavelength of ultraviolet light or the smallest wavelength of visible light. Said pigment comprises at least one defined diffractive structure, the spatial periodicity of which has a spatial period corresponding at least to a multiple of the wavelength of ultraviolet light. In particular, the inventive pigment has a laminar shape. The method for producing such pigments comprises the following steps; a) a defined diffractive structure is created in and/or on a film-type support; b) the defined diffractive structure is coated with a sealant on said support; c) the film-type support processed in steps a) and b) is comminuted so as to form pigment particles. The described pigments have a period of at least several times 400 nm, which means at least 2×400 nm=800 nm. The pigments may have holographic, diffractive microstructures with different orientations of the microstructures. The holographic, diffractive microstructures can even be rotational symmetric. The goal is to realise isotropic first or higher order diffraction in a coating comprising such pigments in a not aligned manner.
U.S. Pat. No. 4,484,797 teaches a variable index-of-refraction optical medium of certain minimum thickness and periodicity with respect to the wavelength of incident light-if it meets certain specified constraints with respect to (1) relative indices-of-refraction of both its internal structure and that of its surroundings and (2) relative values of incident wavelength to periodicity and the relative indices-of-refraction-operates to produce both angularly-dependent subtractive-colour filter reflection spectra and subtractive-colour filter transmission spectra in accordance with its physical parameters. Such filters are suitable for use as authenticating devices for sheet-material authenticated items. They exhibit visible colour effects upon rotating the devices.
Patent document WO2004/077468 teaches a grid structure used for protecting valuable articles through the realization of colour images. The inventive structure consist of at least a first part provided with a grid constant which is less than a wavelength at which said part is observable and embodied in the form of a relief structure whose relief height is defined in such a way that the zero-order grid image can be observed in a determined spectral range. Said part has a size less than 0.5 mm at least in one direction. Preferably, this part has the shape of a line. The optical of the parts of the grid image is tuned by adjusting the grating depth.
EP0105099 teaches a document that includes a substrate which has an outer surface and defines a plane, and a coordinate system which is defined pith respect to the plane. A diffraction-optical authenticating element covers at least part of the outer surface, and generates at least one colour pattern constituting a visually testable feature which verifies the authenticity of the document. The diffraction-optical authenticating element provides a colour pattern moving at a predetermined velocity along a predetermined track when the document is illuminated from a first direction and viewed from a second direction, as defined with respect to the coordinate system, upon the document being rotated within the plane along a prearranged sense of rotation, and at a prearranged velocity. The period of the diffraction-optical authenticating element is in the range of 700 nm to 2200 nm. The colour effect is based on first or higher order diffraction.
Patent document EP1990661 teaches an isotropic zero-order diffractive colour filter, a method to manufacture an embossing tool and a method to manufacture such a filter. The zero-order diffractive colour filter comprises diffractive microstructures and a waveguiding layer, wherein the diffractive microstructures possess a short range ordering over at least four times the period of the microstructures, and the diffractive microstructures possess a long range disordering over length scales of more than 100 μm.